# PHP Program - Find all Prime Numbers in a given Interval

A Prime number is a natural number greater than 1 and divisible by 1 and itself only, for example: 2, 3, 5, 7, etc.

Objective: Write a PHP code to find all prime numbers in a given internal.

### Method 1: Using function to find prime number

In the example below, a function called primenumber() is created which takes a number as argument and checks it for prime number by dividing it with all natural numbers starting from 2 to N/2.

```<?php
\$n = 0;

for(\$i = 2; \$i < (\$MyNum/2+1); \$i++) {
if(\$MyNum % \$i == 0){
\$n++;
break;
}
}

if (\$n == 0){
echo \$MyNum." ";
}
}

\$x = 10;
\$y = 50;
echo "Prime numbers between ".\$x." and ".\$y." are: \n";
for(\$i = \$x; \$i < \$y + 1; \$i++) {
}
?>
```

The above code will give the following output:

```Prime numbers between 10 and 50 are:
11 13 17 19 23 29 31 37 41 43 47
```

### Method 2: Optimized Code

• Instead of checking the divisibility of given number from 2 to N/2, it is checked till square root of N. For a factor larger than square root of N, there must the a smaller factor which is already checked in the range of 2 to square root of N.
• Except from 2 and 3, every prime number can be represented into 6k ± 1.
```<?php
\$n = 0;
if (\$MyNum == 2 || \$MyNum == 3){
echo \$MyNum." ";
}
elseif (\$MyNum % 6 == 1 || \$MyNum % 6 == 5) {
for(\$i = 2; \$i*\$i <= \$MyNum; \$i++) {
if(\$MyNum % \$i == 0){
\$n++;
break;
}
}

if (\$n == 0){
echo \$MyNum." ";
}
}
}

\$x = 100;
\$y = 200;
echo "Prime numbers between ".\$x." and ".\$y." are: \n";
for(\$i = \$x; \$i < \$y + 1; \$i++) {
}
?>
```

The above code will give the following output:

```Prime numbers between 100 and 200 are:
101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
```

5